2 Answers
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Yeah, by the time you have five spokes broken it may be that only one more and it'll collapse (depending on exactly how the broken spokes are arranged). Plus with that many gone the others are under much more serious stress.

In the general case you may have a spoke go now and then and, if you replace it reasonably promptly, it doesn't imply any serious problem. But when spokes are going right and left it usually means that the spokes are nearing end of life and they all need to be replaced.

On a good quality bike with stainless spokes, well cared for (and not abused by jumping, etc), the spokes should last at least 10,000 miles and possibly 30,000. On a lower quality bike, however, with galvanized spokes, corrosion will often do in the spokes before they reach 5,000 miles. And exposure to weather could cut that number in half.

Depending on the quality of the bike it may be cheaper to buy a new/used wheel than to have the existing wheel "relaced". But you need to do one or the other -- that wheel could collapse on you tomorrow.